Bring a large pot of salted water to a boil. Add the linguine and cook until al dente according to package directions (usually about 8–10 minutes). Before draining, reserve ½ cup of pasta water. Drain and set the pasta aside.

In a small bowl, combine Cajun seasoning and smoked paprika. Pat the chicken strips dry with paper towels to ensure a crisp sear. Generously coat the chicken with the spice mix.

Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Once hot, add the chicken strips in a single layer. Cook for 4–5 minutes per side, until golden and cooked through. Transfer to a plate and tent with foil to keep warm.

In the same skillet, reduce heat to medium. Add the remaining 1 tablespoon olive oil and 1 tablespoon butter. Once melted, stir in minced garlic and sauté for 30–60 seconds until fragrant—be careful not to let it brown.

Pour in the heavy cream, bring to a gentle simmer, then reduce heat slightly. Stir in the Parmesan until fully melted and smooth. If the sauce is too thick, add a bit of the reserved pasta water, 1 tablespoon at a time, until it coats the back of a spoon. Season with salt and pepper to taste.

Add the cooked linguine to the sauce and toss well to coat each strand. Gently return the chicken to the skillet and stir to combine. Let everything warm together for 1–2 minutes.

Plate the pasta, topping each portion with sliced Cajun chicken. Garnish with chopped parsley if desired. Serve immediately while the sauce is silky and hot.